John O'Keefe's children's names

It was traditional in UK to name children after family members - grandparents & parents . 

In Ireland, first sons were named after their paternal Grandfather, 2nd sons after maternal Grandfather,   1st daughters often after their maternal Grandmother, 2nd daughters for paternal Grandmother.   Following children would then  named for their parents, oldest uncles and aunts and then other family members. 
Sometimes children were named after family members who had died recently

So for John and O'keefe we have the following:

Mary Anna       1868  Mary - maternal Gt Aunt (religion?) 
                                   Anna - maternal Grandmother & mat aunt
                                   Mary - Gt Gt Grandmother d.1810, but this seems too far back
Helen (Ellen)    1870       -
George             1871   maternal Grandfather
Joseph             1873   maternal Gt Grandfather (religion?)
Eliza                  1875      -
Elizabeth          1877   mother & maternal Gt Grandmother & Gt Aunt
James              1880      -
William Barker 1882  maternal Uncle & Gt Uncle + mother's maiden name
Frances            1886  maternal step-Grandmother
Agnes               1888      -

Note absence of name Richard - paternal Father, maternal Grandfather
Note absence of name John - father
Possibly no Richard or John as only 3 sons

Note:  So   Is Mary named for religioius reasons
                   or is she possibly named for paternal grandmother, John's mother?
             
       who is Helen / Ellen named for? 2nd daughter - John's Mother / Grandmother?
       who is Eliza named for
       who is Agnes named for?